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Largest prime factors of consecutive numbers

Published on Saturday, 19th September 2015, 01:00 pm; Solved by 256;
Difficulty rating: 60%

Problem 526

Let f(n) be the largest prime factor of n.

Let g(n) = f(n) + f(n+1) + f(n+2) + f(n+3) + f(n+4) + f(n+5) + f(n+6) + f(n+7) + f(n+8), the sum of the largest prime factor of each of nine consecutive numbers starting with n.

Let h(n) be the maximum value of g(k) for 2 ≤ kn.

You are given:

  • f(100) = 5
  • f(101) = 101
  • g(100) = 409
  • h(100) = 417
  • h(109) = 4896292593

Find h(1016).